Jacobian Matrix for Basic Local Independence Model

Computes the Jacobian matrix for a basic local independence model (BLIM).

jacobian(object, P.K = rep(1/nstates, nstates),
         beta = rep(0.1, nitems), eta = rep(0.1, nitems),
         betafix = rep(NA, nitems), etafix = rep(NA, nitems))

Arguments

object

an object of class blim, typically the result of a call to blim.

P.K

the vector of parameter values for probabilities of knowledge states.

beta

the vector of parameter values for probabilities of a careless error.

eta

the vector of parameter values for probabilities of a lucky guess.

betafix, etafix

vectors of fixed error and guessing parameter values; NA indicates a free parameter.

Details

This is a draft version. It may change in future releases.

Value

The Jacobian matrix. The number of rows equals 2^(number of items) - 1, the number of columns equals the number of independent parameters in the model.

References

Heller, J. (2017). Identifiability in probabilistic knowledge structures. Journal of Mathematical Psychology, 77, 46–57. doi:10.1016/j.jmp.2016.07.008

Stefanutti, L., Heller, J., Anselmi, P., & Robusto, E. (2012). Assessing the local identifiability of probabilistic knowledge structures. Behavior Research Methods, 44(4), 1197–1211. doi:10.3758/s13428-012-0187-z

See also

blim, simulate.blim, gradedness.

Examples

data(endm)
m <- blim(endm$K2, endm$N.R)

## Test of identifiability
J <- jacobian(m)
dim(J)
#> [1] 15 13
qr(J)$rank
#> [1] 13